Problem: Solve for $x$ and $y$ using elimination. ${-3x-5y = -38}$ ${3x+3y = 24}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $-2y = -14$ $\dfrac{-2y}{{-2}} = \dfrac{-14}{{-2}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {-3x-5y = -38}\thinspace$ to find $x$ ${-3x - 5}{(7)}{= -38}$ $-3x-35 = -38$ $-3x-35{+35} = -38{+35}$ $-3x = -3$ $\dfrac{-3x}{{-3}} = \dfrac{-3}{{-3}}$ ${x = 1}$ You can also plug ${y = 7}$ into $\thinspace {3x+3y = 24}\thinspace$ and get the same answer for $x$ : ${3x + 3}{(7)}{= 24}$ ${x = 1}$